Questions on world-line
in [Relativity]
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From: kenseto on 25 Aug 2006 09:58 "Igor" <thoovler(a)excite.com> wrote in message news:1156435588.287603.157960(a)p79g2000cwp.googlegroups.com... > > kenseto wrote: > > "Igor" <thoovler(a)excite.com> wrote in message > > news:1156353371.333406.159360(a)i42g2000cwa.googlegroups.com... > > > > > > kenseto wrote: > > > > "Igor" <thoovler(a)excite.com> wrote in message > > > > news:1156349832.759078.175940(a)74g2000cwt.googlegroups.com... > > > > > > > > > > kenseto wrote: > > > > > > "Igor" <thoovler(a)excite.com> wrote in message > > > > > > news:1156265582.026355.324580(a)p79g2000cwp.googlegroups.com... > > > > > > The worldline is invariant. Motion is relative. That's all there is > > > to it. Beyond that, I don't really understand what you're even asking. > > > > > What I am asking is: what motion of an object that gives rise to it > > worldline? Is it the object's absolute motion (individual motion)? If not > > why not? > > > > Ken Seto > > Ask Galileo. This is not just an issue with SR. You might want to > reprase your question as "How can motion in space be relative and still > have a well-defined trajectory?" > Of course it is an issue with SR. SR claims that there is only relative motion and the fact that each object has its own world line refute this claim. The world line of an object is due to the individual motion of the object in space.
From: Mike on 25 Aug 2006 11:13 surrealistic-dream(a)hotmail.com wrote: > Mike wrote: > > Paul B. Andersen wrote: > > > Igor wrote: > > > > surrealistic-dream(a)hotmail.com wrote: > > > >> Not true. SR treats accelerations as absolute, but velocites and > > > >> positions as relative. > > > > > > > > Wrong. There is a Lorentz transformation for acceleration also. > > > > > > No, it's correct. > > > But the acceleration that is absolute is the proper acceleration, > > > that is the acceleration measured in the instant inertial > > > rest frame of the object. It is the acceleration that is > > > measured by an accelerometer. This acceleration is absolute, > > > that is independent of frames of reference. > > > The co-ordinate acceleration is however frame dependent. > > > > The term "absolute" implies a much broader range of possibilities than > > simply "independent of FoR". It is better to call proper acceleration > > an invariant. > > Einstein claimed that he left acceleration as "absolute" in SR (that > is, in his generaltization of Newton's mechanics to include > electrodynamics). Why? well, this is partly semantic and partly > historical and they go together. Historically "absolute motion" of any > kind referred to motion with respect to some physically existing space. I agree. > To Newton, acceleration only made sense in his theory if one could > rely on that kind of motion to be with respect to some space in which > absolute accelerations live. So, of course, Newton took the existence > of inertial frames as absolute. And later, Einstein found the inertial > concept wanting, and he introdcued the so-called Principle of > Equivelence in GR. This has nothing to do with absolute motion, i.e. both concepts are also present in Newtonian mechanics and post-Newtonian formulations. > > Anyway, since you mentioned Mach below, I will address his contribution > to relativity here. It was Mach, contrary to what you claimed below, > who got Einstein to doubt the necessity of founding physics on the > concept of absolute acceleration, meaning accelerations with respect to > some invisible, unidentifiably space. Instead, he suggested that the > inertial properties of matter are totally dependent on the distibution > of matter in the universe. And, since the distribution of matter in the > universe is happenstance, it is not depedent on the existence of some > absolute space. > This is a very narrow interpretation. Mach's idea cannot rule out absolute space. You can still have absolute space and inertia dependent on mass distribution in the universe. > Okay, so what is relative about relativity? This: if the equations of > physics are conceptually founded in some theory on motion with respect > to some absolute space, such as the space in which absolute > accelerations live or the space in which absolute velocities live (rest > space of the ether), then the motion is deemed to be "absolute." But if > the equations of physics are founded on the notion of objects relative > to visible (ponderable) matter, the theory is said to be > "relativistic." Nowadays, physics includes the notion of invisible > matter/energy but such things are still object like (in the same way > that ponderable matter is), not space like in the way the the rest > frame of the ether is. You are confusing Relational theories of spacetime and motion with Relativistic theories. This is a very common mistake. Relativistic theories do not preclude absolute space. Actually, it is now understood that the spacetime of SR and GR is absolute. Relational theories preclude absolute space time but there is no theory at hand which is founded on purely relational spatiotemporal quantities. It is impossible to do it since it is impossible to know the mass distribution function of the universe. Esxpecially when more than 70% (or 90% nobody knows) is ssome dark matter. > > Einstein's main boasting point for SR, was not E = mc^2, but that he > got rid of absolute velocities. And his main boasting point of GR was > not curved spacetime, but that he got rid of absolute accelerations. Neither. This is another common misunderstanding. newtonian Mechanics do not need absolute velocities either. Galilean transformations can live with relative velocities leaving only acceleration absolute, Furthermore, it is true that while gravitational accelerations are eliminated in GR, any deviations from geodesic motion can only be treated absolutely and os is rotational motion, which is an unsolved puzzle. > > > > However, this whole thing is a math trick. There is no > > physical significance to an "instant inertial rest frame co-moving with > > an object". In lieu of the math trick, acceleration must be referenced > > wrt an absolute space of some kind or wrt the mass distribution in the > > universe as Mach insisted, which makes any attempt to develop a > > relativity theory hopeless. > > Just the opposite from Mach, the relativist. No, I said this is a misconception of people with a shallow understanding of the subject. Mach was a Relationist, not a Relativist. Do not confuse the two terms, they mean two different things. Mike > > > > > What this instant inertial frame means essentially, is that any > > accelerated motion can be broken down to a series of inertial motions, > > something that is totally absurd. This error has been pointed out by > > many as back as 300 years ago, before Einstein and SR. It turns out > > that while the thinking is wrong the result turns out correct > > accidentaly. > > > > There is no way to define an instant inertial frame because an instant > > in the motion of an object cannot be defined. Motion is continuous to > > arbitrary accuracy. > > > > Mike
From: YBM on 25 Aug 2006 11:41 kenseto a ?crit : > "YBM" <ybmess(a)nooos.fr> wrote in message .... >>So what ? In that case (Seto at rest in F), my definition works as well >>and gives { (x_s,y_s,z_s,t) / t \in R } where (x_s,y_s,z_s) is your >>constant spacial coordinates... > > > You keep on using F as a reference for me. I can have a world line without > any reference. F can see that I have a different world line after I > accelerated. But that's because I changed my state of absolute motion. Please define what a world line is without reference to a given frame. >>BTW, you seem (in another post of this thread) to suggest that a >>worldline could be defined without refering to a frame. Please do so.
From: PD on 25 Aug 2006 12:42 kenseto wrote: > In SR the world line is the path of an object in space with the passage of > time. Each object has its own world-line. > Questions: > 1. Does this mean that the world-line of an object is the result of the > individual motion of the object? Not at all. A worldline's slope is indicative of the object's velocity *in a particular* frame of reference. By choosing a different frame of reference, the slope of the line changes. In fact, for a particular frame of reference, the world line's slope indicates no motion. PD > 2. SR says that there is no such thing as individual motion. There is only > relative motion then how does an individual object have world-line? See above. The slope of the world line is motion *with respect to* a reference point in the frame. > > Ken Seto
From: PD on 25 Aug 2006 12:44
kenseto wrote: > "Igor" <thoovler(a)excite.com> wrote in message > news:1156265582.026355.324580(a)p79g2000cwp.googlegroups.com... > > > > kenseto wrote: > > > In SR the world line is the path of an object in space with the passage > of > > > time. > > > > Not quite. It's literally the path taken through spacetime. > > > > >Each object has its own world-line. > > > > Yes. > > > > > > > Questions: > > > 1. Does this mean that the world-line of an object is the result of the > > > individual motion of the object? > > > > Yes, through spacetime, but as opposed to what? > > > > > 2. SR says that there is no such thing as individual motion. > > > > Depends on what you mean by individual motion. If you mean absolute, > > then you're correct. > > > > >There is only > > > relative motion then how does an individual object have world-line? > > > > The world line is fixed in spacetime. It's invariant, so everyone > > agrees on the path. How you define the coordinate system, however, is > > entirely up to you. That's where relative motion comes in. > > > The question is: how does an object have world line? What make it trace out > a world line? What makes a stop sign go backwards when I pass it in my car? |